{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ADDING SINE WAVES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "t=np.arange(0,10,0.1)\n",
    "\n",
    "a1=np.sin(t)\n",
    "a2=np.sin(2*t)\n",
    "a3=np.sin(3*t)\n",
    "a4=a1+a2+a3\n",
    "\n",
    "plt.subplot(4,1,1)\n",
    "plt.plot(a1)\n",
    "plt.title('sine wave 1')\n",
    "plt.subplot(4,1,2)\n",
    "plt.plot(a2)\n",
    "plt.title('sine wave 2')\n",
    "plt.subplot(4,1,3)\n",
    "plt.plot(a3)\n",
    "plt.title('sine wave 3')\n",
    "plt.subplot(4,1,4)\n",
    "plt.plot(a4)\n",
    "plt.title('sum of sine waves')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CONVOLUTION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "[1 2 3 4 5 0 0 0 0 0]\n",
      "[ 2  4  6  8 10  0  0  0  0  0]\n",
      "[2, 8, 20, 40, 70, 88, 92, 80, 50, 0]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x800 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x=(1,2,3,4,5)\n",
    "h=(2,4,6,8,10)\n",
    "\n",
    "c=len(x)+len(h)\n",
    "print(c)\n",
    "\n",
    "x=np.pad(x,(0,c-len(x)))\n",
    "h=np.pad(h,(0,c-len(h)))\n",
    "print(x)\n",
    "print(h)\n",
    "\n",
    "y=[0]*c\n",
    "\n",
    "for n in range(0,c):\n",
    "    for k in range(0,c):\n",
    "        y[n]=y[n]+h[k]*x[n-k]\n",
    "\n",
    "print(y)\n",
    "\n",
    "plt.figure(figsize=(6,8))\n",
    "\n",
    "plt.subplot(6,1,1)\n",
    "plt.plot(x)\n",
    "plt.title('Continuous')\n",
    "plt.subplot(6,1,2)\n",
    "plt.plot(h)\n",
    "plt.subplot(6,1,3)\n",
    "plt.plot(y)\n",
    "\n",
    "plt.subplot(6,1,4)\n",
    "plt.stem(x)\n",
    "plt.title('Discrete')\n",
    "plt.subplot(6,1,5)\n",
    "plt.stem(h)\n",
    "plt.subplot(6,1,6)\n",
    "plt.stem(y)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CROSS CORRELATION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Define two sequences\n",
    "x = np.array([1, 2, 3, 4, 5])\n",
    "h = np.array([2, 4, 6, 8, 10])\n",
    "\n",
    "# Lengths of the sequences\n",
    "N = len(x)\n",
    "M = len(h)\n",
    "L = N + M - 1  # Length of the resulting sequence after correlation\n",
    "\n",
    "# Zero-pad sequences to match the length for correlation\n",
    "x_correlation = np.pad(x, (0, L - N))\n",
    "h_correlation = np.pad(h, (0, L - M))  # Pad 'h' without reversing for correlation\n",
    "\n",
    "# Compute correlation\n",
    "y_correlation = np.zeros(L)\n",
    "for n in range(L):\n",
    "    for k in range(N):\n",
    "        if n - k >= 0 and n + k < M:\n",
    "            y_correlation[n] = y_correlation[n]+ x_correlation[k] * h_correlation[n + k]\n",
    "\n",
    "# Plotting\n",
    "plt.figure(figsize=(8, 6))\n",
    "\n",
    "plt.subplot(3, 1, 1)\n",
    "plt.stem(x_correlation)\n",
    "plt.title('Sequence x[n]')\n",
    "\n",
    "plt.subplot(3, 1, 2)\n",
    "plt.stem(h_correlation)\n",
    "plt.title('Sequence h[n]')\n",
    "\n",
    "plt.subplot(3, 1, 3)\n",
    "plt.stem(y_correlation)\n",
    "plt.title('Cross-Correlation Result')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "AUTO CORRELATION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Define a sequence\n",
    "x = np.array([1, 2, 3, 4, 5])\n",
    "\n",
    "# Length of the sequence\n",
    "N = len(x)\n",
    "L = 2 * N - 1  # Length of the resulting autocorrelation sequence\n",
    "\n",
    "# Zero-pad the sequence for autocorrelation\n",
    "x_autocorr = np.pad(x, (0, N - 1))\n",
    "\n",
    "# Compute autocorrelation\n",
    "y_autocorr = np.zeros(L)\n",
    "for n in range(L):\n",
    "    for k in range(N):\n",
    "        if n - k >= 0 and n + k < N:\n",
    "            y_autocorr[n] += x_autocorr[k] * x_autocorr[n + k]\n",
    "\n",
    "# Plotting\n",
    "plt.figure(figsize=(8, 6))\n",
    "\n",
    "plt.subplot(3, 1, 1)\n",
    "plt.stem(x_autocorr)\n",
    "plt.title('Sequence x[n]')\n",
    "\n",
    "plt.subplot(3, 1, 2)\n",
    "plt.stem(x_autocorr)\n",
    "plt.title('Sequence x[n]')\n",
    "\n",
    "plt.subplot(3, 1, 3)\n",
    "plt.stem(y_autocorr)\n",
    "plt.title('Autocorrelation Result')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
